The questions below dealing with quadratic functions have been selected from various state and national assessments. Although this lesson may not fully equip students with the ability to answer all such test questions successfully, students who participate in active lessons like this one eventually will develop the conceptual understanding needed to succeed on these and other state assessment questions.

Taken from the Ohio Grade 12 Proficiency Test (February 2001):

If x2 + ax + a2/4 = 0, then x = ?

A. - a/4B. - a/2 (correct answer)
C. a/2
D. a/4

Taken from the Maryland High School Assessment in Algebra, Grade 11 (2002):

Doug makes a rectangular dog pen using 8 yards of fencing. The graph below shows the relationship between the width of the pen and the area of the pen. In the ordered pair (2, 4), what does the y-coordinate represent?

A. maximum area of the pen (correct answer)
B. maximum width of the pen
C. maximum length of the pen
D. maximum perimeter of the pen